### Abstract

A closed solid body separates one point set from another if it contains the former and the closure of its complement contains the latter. We present a near-linear algorithm for deciding whether two sets of n points in 3-space can be separated by a prism, near-quadratic algorithms for separating by a slab or a wedge, and a near-cubic algorithm for separating by a double-wedge. The latter three algorithms improve the previous best known results by an order of magnitude, while the prism separability algorithm constitutes an improvement of two orders of magnitude.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 675-683 |

Number of pages | 9 |

Volume | 15 |

State | Published - 2004 |

Event | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States Duration: Jan 11 2004 → Jan 13 2004 |

### Other

Other | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
---|---|

Country | United States |

City | New Orleans, LA. |

Period | 1/11/04 → 1/13/04 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Discrete Mathematics and Combinatorics
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms*(Vol. 15, pp. 675-683)

**Efficient Algorithms for Bichromatic Separability.** / Agarwal, Pankaj K.; Aronov, Boris; Koltun, Vladlen.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms.*vol. 15, pp. 675-683, Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA., United States, 1/11/04.

}

TY - GEN

T1 - Efficient Algorithms for Bichromatic Separability

AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Koltun, Vladlen

PY - 2004

Y1 - 2004

N2 - A closed solid body separates one point set from another if it contains the former and the closure of its complement contains the latter. We present a near-linear algorithm for deciding whether two sets of n points in 3-space can be separated by a prism, near-quadratic algorithms for separating by a slab or a wedge, and a near-cubic algorithm for separating by a double-wedge. The latter three algorithms improve the previous best known results by an order of magnitude, while the prism separability algorithm constitutes an improvement of two orders of magnitude.

AB - A closed solid body separates one point set from another if it contains the former and the closure of its complement contains the latter. We present a near-linear algorithm for deciding whether two sets of n points in 3-space can be separated by a prism, near-quadratic algorithms for separating by a slab or a wedge, and a near-cubic algorithm for separating by a double-wedge. The latter three algorithms improve the previous best known results by an order of magnitude, while the prism separability algorithm constitutes an improvement of two orders of magnitude.

UR - http://www.scopus.com/inward/record.url?scp=1842487370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842487370&partnerID=8YFLogxK

M3 - Conference contribution

VL - 15

SP - 675

EP - 683

BT - Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms

ER -